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  • Measurement of the intensity of progressive ultrasonicwaves by means of Raman-Nath diffractionStapper, M.

    Published: 01/01/1974

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    Citation for published version (APA):Stapper, M. (1974). Measurement of the intensity of progressive ultrasonic waves by means of Raman-Nathdiffraction. (EUT report. E, Fac. of Electrical Engineering; Vol. 74-E-53). Eindhoven: Technische HogeschoolEindhoven.

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    Download date: 07. Sep. 2018





    Drs. M. Stapper

  • Gro~i!r Mea;sutenrellt and Control

    Dep1rt'tmE!'nt elf Electrical Engineering

    Eindhoven University of Technology

    Eind:hoven; The Netherlands





    Drs. M. Stapper

    T.H. Report 74--53

    November '74

    ISBN 90 6144 053 X

  • ""So'''',: .

    - 1 -



    I. Introduction

    2. Derivation of the diffraction equation

    3. Cqnsiderations on the diffraction equation

    3.1. Parameters

    3.2. The physical consistency of the solutions

    3.3. The analytic availability of the solutions

    4. Solutions of the diffraction equation

    4.1. aaman-Nath condition

    4.2. Bragg condition

    4.3. Summary

    5. Quantum-mechanical approach to the diffraction


    6. Experiments

    Appendix A. Aspects of general wave theory

    Appendix B. Numerical methods. for computing the value

    of v.

    Appendix C. Abel inversion

    Appendix D. The sound intensity



    List of symbols

    . " :'-'>""x!-.,~ '.~-~:, ",-






















  • - 3 -


    Sometimes it may be desirable to measure directly the acoustical inten--

    sity of an ultrasonic sound beam. One of the methods that can be used

    for this measurement is to analyse the diffraction pattern occurring

    whenever coherent light is passing through a sound field.

    In this report the theory of this diffraction phenomenon is treated.

    A differential equation is derived describing the diffraction process.

    The solutions of this,equation are discussed.

    In this discussion the physical backgrounds to the differential equation

    and its parameters are continuously st,essed. The insight into the phy-

    sical significance of the diffraction process is deepened further by also

    describing it from a quantum-mechanical point of view. It turns out to be

    possible to describe a sound field as a stream of quasi-particles: phonons.

    From this point of view diffraction is to be considered an interaction

    between photons and phonons.

    'Finally, a number of experiments are discussed that have been made in

    order to verify some of the theoretical results.

  • - 4

    1. Introduction.

    1.1. i

    In recent years ultrasound is meetingiwith the ever increasing interest i

    of the~ medical world. Its range of applications is still broadening. ,

    At p~resent ultrasound is being us.ed iii diagnosis as well as in therapy. I

    A few examples of diagnostic applications are: I

    - echography, as used in neurology, obstetrics, cardiology,. ophthalmology,


    - measurement of blood velocity using'Doppler shift.

    - measurement of ~ flow rates in re~piratory physiology.

    measurement of foetal heart rate inill!idwivery.

    The frequency-band used extends from 1 to 10 Me.

    In the therapeutic field ultrasound is not so widely used.

    Some examples:

    Narrow ultrasonic beams of high intensity are sometimes used in neurosur-

    gery to destroy malfunctioning areas 1n the brain or in the treatment of

    Meniere's disease by destruction of the labyrinth. In dentistry low

    frequency ultrasound can be used for cleaning purposes.

    Thermal effects make ultrasound useful as a substitute for diathermic


    Excellent reviews of the medical applications of ultrasonic radiation

    can be. found in .the references. 1, 2, 3 and 4.

    In medicine ultrasound has to be used with some care. Biological tissues

    may be harmed by too high intensities. The ensuing damage may be thermal

    in origin (overheating due to the absorption of sound) or

    (e.g. hemolysis). Tissue damage also can occur through; disintegration

    of proteins or cell organells or through cavitation effects (gas embolism).

    Though a great deal of research has been done on the harmful effects of

    ultrasonic radiation as well as on the height of the maximum allowed dose,

    there is however at present no conclusive answer to the ques~tion of

    how much ultrasound an organ can tolerate without being damaged. One of

    the technical problems in this field is the difficulty of directly mea-

    suring the acoustical intensities in ~iquid biological material.

    , "'-,

  • - 5 -

    This report aims to contribute to these measuring techniques thus

    hoping to be of some help in overcoming the existing difficulties.

    From literature we know of quite a number of methods being used for mea-

    suring acoustical intensities in a more or less direct way (ref. 6, 7,

    8,9, 10).

    Some.of these methods:

    1. the calorimeter method, in which the increase of temperature is

    measured in a medium that completely absorbs the ultrasonic wave.

    This method is te~hnically difficult, not very accurate and can

    only be applied to high sound intensities.

    '2. the measurement of the Langevin ra4iation pressure caused by the

    sound field. This method is also rather difficult because of the

    very small values of this kind of pressure. Moreover the theoretical

    background to radiation pressure has not as yet been very firmly es-

    tablished in literature.

    3. the method using the reciprocity principle. The efficiency of an

    ultrasonic transducer can be measured by the emission of a short

    wave train which having been reflected must be received again by

    the same transducer. A difficulty in this method lies in the trans-

    mission of short, sharply limited wave packets.

    4; the optical method. This method makes use of the fact that a sound

    field will act as a phase grating to any beam of coherent light

    falling through it perpendicularly.

    The latter method has compared to the former ones the following advantages:

    1. A light beam is used as a measuring probe. Since the wavelength of the

    light is very small compared to the wavelength of the sound, the sound

    field will scarcely be disturbed by the measuring action. The object

    to be measured is influenced by the measurement but to a negligible


    2. When a laserbeam is used as a light beam its small diameter permits

    the measurement of local sound intensities instead of only measuring

    intensities averaged over the gross area of the sound field. Thus

    it becomes possible to scan the sound field in small steps probing

    the spatial distribution of acoustic energy in this field.

  • - 6 , ,

    3. The method not only gives informJion on the intensity of ",the sound

    b 1 . f C 11" "h' I ut a so on 1tS wave orm. onsequent y 1t g1ves 1ns1g t 1nto t,e I '

    degree to which the sound wave ha~ been distorted. 1

    4. From an instrumental point of vie~ this method is a very--simpl'e one., ,

    The following disadvantages have to b~ mentioned also: I

    1. The method is rather time-conswni~g, due t